The $��$-$��$ reflection symmetry serves as a unique basis for understanding the observed neutrino mixing as it can lead us to the interesting results $��^{}_{23} = ��/4$ and $��= -��/2$ which stand close to the current experimental results. But a precise measurement for $��^{}_{23}$ and $��$ will probably force us to modify the neutrino mixing $U^{(0)}$ from such a symmetry. Here we perform a study for modifications to $U^{(0)}$ in the forms of $U^{(1)\dagger} U^{(0)}$ and $U^{(0)} U^{(1)}$ where $U^{(1)}= R^{(1)}_{ij}$ (for $ij = 12, 23$ and 13) with $R^{(1)}_{ij}$ denoting a real orthogonal rotation on the $ij$ plane.

16 pages, 6 figures, minor revision, references added, to appear in Nuclear Physics B